Question

solve
$\cos( {cos}^{ - 1} ( \frac{ - \sqrt{3} }{2} )+ \frac{\pi}{6} )$

Answer 1

This is the question of inverse trigonometry. So the formulas of inverse trigonometry are used.

$\cos( { \cos }^{ - 1} ( \frac{ - \sqrt{3} }{2} ) + \frac{\pi}{6} ) \\ \\= \cos( { \cos }^{ - 1} ( - \cos \frac{\pi}{6} ) + \frac{\pi}{6} ) \\\\ = \cos(\pi - { \cos }^{ - 1} cos \frac{\pi}{6} + \frac{\pi}{6} ) \\\\ = \cos(\pi - \frac{\pi}{6} + \frac{\pi}{6} )\\ \\ = \cos(\pi) \\\\ = - 1$